Physics Question

[sailorchic34]

Originally Posted by jkishel

When the same person climbs steps on the moving escalator, the same amount of work is expended, wh, some by the person and the rest by the escalator, again neglecting the negligible work expended in the horizontal direction.

The escalator reduces the amount of work required by a person to climb a flight of stairs, down to zero if the person just stands stationary on the escalator. That's why we have escalators.

But the work done by a person stepping up the step on a moving escalator is the same work required by a man taking a step up on stairs. That was the question.

Besides the escalator is doing far more work, that is, it is less efficient then a man climbing the stairs. Partly due to motor efficiency and power factor, but also due to friction in the drive system, bearings, linkage friction, etc.

The average man uses 0.02watts (.17 calories) to climb one step. the average escalator is using 7.5 hp or about 7000 watts (with power factor) or 1.9 watts a second. So if the man climbs two steps in one second he's using .04 watts while the escalator is using 47 times that much. So a man walking up steps uses less energy then an escalator.

[jkindredpdx]

Originally Posted by sailorchic34

But the work done by a person stepping up the step on a moving escalator is the same work required by a man taking a step up on stairs. That was the question.

Besides the escalator is doing far more work, that is, it is less efficient then a man climbing the stairs. Partly due to motor efficiency and power factor, but also due to friction in the drive system, bearings, linkage friction, etc.

The average man uses 0.02watts (.17 calories) to climb one step. the average escalator is using 7.5 hp or about 7000 watts (with power factor) or 1.9 watts a second. So if the man climbs two steps in one second he's using .04 watts while the escalator is using 47 times that much. So a man walking up steps uses less energy then an escalator.

That's not even counting the energy expended by facilities to repair the breakdowns or the energy to manufacture and deliver the parts and ...

[sy_gilana]

This is all a lot of fun, and Sailorchick continues to blow my socks off, oh wait, I don't have any.

BUT

How do you use the escalator analogy to explain sailing?

You would expend the same amount of energy if the concrete step was the same height as the moving metal one. YOU the "MAN" will raise the same mass the same height. The fact that the escalator is in motion is irrelevant in the scenario described, assuming that things like vectored wind resistance and distance from the center of the earth is ignored as it should be...

I explain sailing to non sailors using the kite-flying analogy.

[sailorchic34]

Originally Posted by jkindredpdx

I believe you... it just seems that from the time I set my forward foot down and start lifting my body, the step moves toward me. Color me

Ah you know, down is interesting. because your stepping forward and up while the step is moving backwards and down. The net effect is your using less energy as your not lifting as high per step. I think that only applies to going up the down escalator.

[jkishel]

Work required to climb a step is the same whether the step is moving or stationary. The person has lifted him or herself the height of one step.

[DefinitelyMe]

OK, i think this is sound.........

Gravitational potential energy gained by lifting an object (which is the same as the energy required to do the work in the first place (this is the only time i will mention work, which is a physics term related to energy)):

E = mgh

Where E is the energy in Joules, m is the mass of the object in Kg, g is acceleration due to gravity and h is the height in meters. Let's say our escalator takes someone 10m vertically, and there's a set of stairs next to it. Let's say our person is fat and weighs 100Kg. Let's also simplify acceleration due to gravity and call it 10m/s/s.

In both cases, E = 100x10x10 = 10000J. That's the same for the escalator or the stairs. Now, in the stairs example, that energy is all contributed by the person. In the escalator example, it's all contributed by the electric motor in the escalator.

This is where is gets tricky. If a person walks up the escalator then some of the energy is provided by the person and some is provided by the escalator, so the total amount of energy expounded by the person is less than if they were walking up the stairs, but more than if they were to stand still on the escalator FOR ANY GIVEN RISE IN HEIGHT.

OK, now let's make our escalator and our steps infinitely long and have people walking up each of them. Let's say that the person walking up the steps is going up 0.2m with every step. They have expounded mgh = 100x10x0.2 = 200J of energy for each step. Now, let's say the the escalator is moving upwards at the same rate that the people are walking at, and the steps on the escalator are the same size as the stationary steps. For every step he takes, he's going 0.2m, plus the 0.2m that the escalator has moved. Remember , he's stepping at the same rate as the guy on the non-moving steps. He's stepping up 0.2m, so he's used 200J to do so, and the escalator has moved him up 0.2m in that time, so the escalator has used 200J of energy.

The net result is that the guy on the escalator expounds the same amount of energy per step as the guy doing it manually, but in this example he moves upward at twice the rate.

Finally, previous posters, and experience from having done this in the real world, tell's us that it is indeed harder, but that is only true for the very first step, and it's because the person going up the stairs has to accelerate up to a speed of 0.2m/s but the person on the escalator has to accelerate up to 0.4m/s. The force required to do so (F=ma) is twice as much for the guy on the escalator. Regardless of whether that force is being generated by the person themselves or the escalator, it must be experienced by the person, since it is the person that is being accelerated. It's exactly the same as any other acceleration. Stand in a lift (elevator for americans). You experience a force on your body as the lift accelerates or decelerates (positive and negative respectively) but while it's moving at a constant rate you experience no net force. The same same goes for accelerating in a car, or a rocket, or an airplane or anything else. You only experience the force during acceleration and deceleration.

I can't think of a single escalator that exists in my entire country so i can't try it, but give it a go wherever you are! Just don't get locked up as a crazy person for going up and down the same escalator repeatedly!

[DeepFrz]

Originally Posted by sailorchic34

Ah you know, down is interesting. because your stepping forward and up while the step is moving backwards and down. The net effect is your using less energy as your not lifting as high per step. I think that only applies to going up the down escalator.

That would only apply at the bottom or top of the escalator. In between the first few and last few steps the energy transformed would be the same as walking up a stationary staircase.

[DefinitelyMe]

I'm trying to think how this applies to sailing........... the closest i can get is in dealing with speed over ground as it compares to speed through the water. It takes the same amount of energy to go at 5 knots through the water, but if you're in a 5-knot adverse current you aren't going to go anywhere, just like walking up an escalator going the wrong way. On the other hand if the current is with you you'll be doing 10 knots over ground, but still harnessing just as much energy in your sails as the guy not going anywhere. Any other examples anyone?

[sailorchic34]

Originally Posted by DeepFrz

That would only apply at the bottom or top of the escalator. In between the first few and last few steps the energy transformed would be the same as walking up a stationary staircase.

That's what I initially thought too. But as your stepping up, the step is moving down, so the net effect is the step is just a bit shorter. This as when your stepping up on the step, the the step at the same time is moving down. So a 9 inch riser as your lifting the body, is moving down and the net is your only lifting ~8" inches or so rather then 9". It depends on the overall height of the step and and speed down.

[Stu Jackson]

Originally Posted by jkindredpdx

Thanks all... (and yes I could have googled it, but I trust y'all so much more)

So If I'm in a rocket blasting off (a few feet from the surface) of the earth I would use no more energy than climbing a ladder while the rocket was sitting on the launch pad?

No.

My first answer on page one mentioned acceleration. If the "thing" you're on is accelerating, it would be different.

Once the acceleration is over, then it's the same.

I know you never stand up in an airplane when it's taking off or landing, but imagine you did (or could ). When walking forward on take-off, it'd be harder, right?

If static, like only AFTER you get on the escalator, then it's the same.

Ever get on a moving walkway (i.e., people mover, found at many large airports)? Same thing. Once you're ON IT, it's no different walking forward than on dry land. You only get a feeling of difference when you get on or off, which is when you're changing speeds, which is also acceleration or deceleration.

[Stu Jackson]

Originally Posted by sailorchic34

That's what I initially thought too. But as your stepping up, the step is moving down, so the net effect is the step is just a bit shorter. This as when your stepping up on the step, the the step at the same time is moving down. So a 9 inch riser as your lifting the body, is moving down and the net is your only lifting ~8" inches or so rather then 9". It depends on the overall height of the step and and speed down.

Could it be only if you JUMP?

[Caribbeachbum]

Originally Posted by skipmac

Don't think I agree with this. Work is defined by force and distance. In this case the same weight of your body is moved the same distance (assuming stairs and escalators are the same) so the total work done by the escalator + walking will be the same as the work done by walking alone up fixed stairs. Time nor speed change the amount of work done.

Perhaps I worded it poorly -- I was, in the second paragraph, referring to the system as a whole. Your step up applies force in the opposite direction, which the escalator system must compensate for in order to maintain its constant velocity.

[Weyalan]

I think it will depend on the speed of the escalator. If the speed of the escalator is very very fast, say, some significant proportion of the speed of light, then Lorentz Contraction will effectively reduce the length of the steps in the direction of movement, so that the total energy expended in that step will be less than in a static or low velocity frame of reference (c.f. the Mu Meson Experiment).

I'll get my hat and coat....

[barnakiel]

We need energy to shoot up a sputnik but a sputnik will fall down by itself.

Same story with an escalator - one needs more energy per step when the escalator is moving up.

b.

[sailorchic34]

Originally Posted by Weyalan

I think it will depend on the speed of the escalator. If the speed of the escalator is very very fast, say, some significant proportion of the speed of light, then Lorentz Contraction will effectively reduce the length of the steps in the direction of movement, so that the total energy expended in that step will be less than in a static or low velocity frame of reference (c.f. the Mu Meson Experiment).

I'll get my hat and coat....

.

But if your on the escalator at tau 0.7, from your reference frame, nothing has changed. It's only from an external reference frame that there is contraction.

I think I have come to the conclusion that the OP is a evil evil man. Such a simple question and zoom, we run smack into reference frames and general relativity.